Abstract

By use of the Kubelka-Munk theory, the Mie theory and the independent scattering approximation, we obtain the explicit expression of the emittance of an infrared coating attached to a radar absorber with a high emittance, in the 3~5μm window. Taking aluminum particles with spherical shape as the pigments within the coating, we give the dependence of the coating emittance with respect to the particle radius, the thickness of the coating. At a volume fraction of 0.05, we propose the optimum particle radius range of the pigment particles is around 0.35~0.6μm. When the thickness of the coating exceeds 300μm, the decrease of emittance at 4μm wavelength becomes negligible. Too much thickness of IR layer wouldn’t contribute to the decrease of emittance. We study the influence of the infrared coating on the performance of the radar absorber, and believe that not too much thick infrared coating consisting of spherical Al particles wouldn’t result in a remarkable deterioration of the absorbing ability of the radar absorber.

© 2005 Optical Society of America

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References

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  8. C. F. Bohren and D.F. Huffman, Absorption and Scattering of Light by Small Particles, (New York: Willey, 1983).
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  14. E. D. Palik, Handbook of Optical Constants of Solids, (New York: Academic, 1985).
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  16. E. S. Thiele and R. H. French, "Computation of light scattering by anisotropic spheres of rutile titania," Adv. Mater. 10, 1271-1276 (1998).
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  17. W. E. Vargas and G. A. Niklasson, "Generalized method for evaluating scattering parameters used in radiative transfer models," J. Opt. Soc. Am. A 14, 2243-2252 (1997).
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  18. M. I. Mishchenko et al. Scattering, Absorption, and Emission of Light by Small Particles, (Cambridge, 2002) Chapter 3.
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Adv. Mater. (1)

E. S. Thiele and R. H. French, "Computation of light scattering by anisotropic spheres of rutile titania," Adv. Mater. 10, 1271-1276 (1998).
[CrossRef]

AIAA J. (1)

H. C. Hottel, A. F. Sarofim, W. H. Dalzell, and I. A.Vasalos , "Optical properties of coatings. Effect of pigment concentration," AIAA J. 9, 1895-1898 (1971).
[CrossRef]

Ann. Phys. (1)

G. Mie, "Beitrâge zur optik truber Medien, speziell kolloidaler Metallosungen,"Ann. Phys. 25, 377-452 (1908).
[CrossRef]

Appl. Opt. (4)

IEEE T. Magn. (1)

K. Kim, W. Kim, and S. Hong, "A study on the behavior of laminated electromagnetic wave absorber," IEEE T. Magn. 29, 2134-2138 (1993).
[CrossRef]

J. Heat Transfer (1)

M. Q. Brewster, and C. L. Tien, "Radiative transfer in packed fluidized beds: dependent versus independent scattering," J. Heat Transfer 104, 573-579 (1982).
[CrossRef]

J. Opt. Soc. Am A (1)

W. E. Vargas and G. A. Niklasson, "Generalized method for evaluating scattering parameters used in radiative transfer models," J. Opt. Soc. Am. A 14, 2243-2252 (1997).
[CrossRef]

J. Opt. Soc. Am. (1)

J. Opt. Soc. Am. A (1)

J. Phys. F: Metal Phys. (1)

A.G. Mathewson and H.P. Myers, "Optical absorption in aluminium and the effect of temperature," J. Phys. F: Metal Phys. 2, 403-415 (1972).
[CrossRef]

J. Res. National Bureau Standards-C. (1)

J. C. Richmond, "Relation of emittance to other optical properties," J. Res. National Bureau Standards-C. 67C, 217-226 (1963).

Z. Tech. Phys. (1)

P. S. Kubelka and F. Munk , "Ein Beitrag zur Optik des Farbanstriche," Z. Tech. Phys. 12, 593-601 (1931).

Other (5)

M. F. Modest, Radiative heat transfer, (New York: McGraw-Hill, 1993).

A. Ishimaru, Wave Propagation and Scattering in Random Media, (Academic, 1978).

C. F. Bohren and D.F. Huffman, Absorption and Scattering of Light by Small Particles, (New York: Willey, 1983).

M. I. Mishchenko et al. Scattering, Absorption, and Emission of Light by Small Particles, (Cambridge, 2002) Chapter 3.

E. D. Palik, Handbook of Optical Constants of Solids, (New York: Academic, 1985).

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Figures (6)

Fig. 1.
Fig. 1.

The structure of a radar absorber coated with an infrared layer.

Fig. 2.
Fig. 2.

(a) The extinction efficiency, scattering efficiency, backscattering efficiency (1-σc )Q sca, and absorption efficiency vs. radius of pigment particle incident by 3μm, 4μm and 5μm light respectively. It should be noted that the absorption is very weak relative to scattering in non-Rayleigh regime, and Q ext, Q sca almost overlap. (b) Emittance of coating layer vs. radius of pigment particle. The particle volume fraction and thickness of the layer are put to 0.05, and 0.5mm.The emittance of RAM layer is put to 0.9. When a≥0.2μm, independent scattering dominates, and our approach is valid. When a<0.2μm (for λ=3μm), the dependent scattering isn’t negligible, but we treat this still by independent scattering approach. In addition, the PDRA may be challenged in this region. So the relation of emittance to particle radius maybe deviates markedly from practice in this region.

Fig. 3.
Fig. 3.

(a) The angular dependence of the illumination internal to the IR layer: λ=4μm and a=0.2, 0.6μm; (b) The dependence of the optical depth of 500μm thick layer with respect to the particle radius (corresponding to Fig. 2(b)).

Fig. 4.
Fig. 4.

Emittance of the radar absorber coated with an IR layer with different thickness vs. particle radius. λ=4μm.

Fig. 5.
Fig. 5.

(a) Real part of Al dielectric function; (b) Imaginary part of Al dielectric function; (c) Real part of the effective dielectric function of IR layer; (d)Imaginary part of the effective dielectric function of IR layer.

Fig. 6.
Fig. 6.

(a) The dielectric permittivity, (b) magnetic permeability of RAM layer. (c) The Influence of IR layer consisting of spherical Al particles on the performance of the radar absorber. The blue solid line describes the radar reflectivity of RAM; The green dashed denotes the radar reflectivity of radar absorber coated with an additional IR layer. The thickness of RAM layer is 1mm and that of IR layer is 0.3mm. The thickness of IR layer is a saturation thickness.

Tables (1)

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Table 1. The refractive index of aluminum in 3~5 μm window

Equations (20)

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ε = 1 R e ( 1 R e ) ( 1 R i ) R v ( 1 R v R RAM ) ( 1 R e ) ( 1 R i ) ( R v R RAM ) exp ( 2 γ d 1 ) ( 1 R i R v ) ( 1 R v R RAM ) ( R v R i ) ( R v R RAM ) exp ( 2 γ d 1 ) ,
{ R v = 1 + K S [ ( K S ) 2 + 2 ( K S ) ] 1 2 γ = K 2 + 2 K S .
R e = 1 2 + ( m 1 1 ) ( 3 m 1 1 ) 6 ( m 1 + 1 ) 2 + m 1 2 ( m 1 2 1 ) 2 ( m 1 2 + 1 ) 3 ln ( m 1 1 ) ( m 1 + 1 ) 2 m 1 3 ( m 1 2 + 2 m 1 1 ) ( m 1 2 + 1 ) ( m 1 4 - 1 ) + 8 m 1 4 ( m 1 4 + 1 ) ( m 1 2 + 1 ) ( m 1 4 1 ) 2 ln m 1 ,
S ( 0 ) = 1 2 n = 1 ( 2 n + 1 ) ( a n + b n ) = 0 ,
ε EMG = ε h [ ε p + 2 ε h + 2 f ( ε p ε h ) ] ( 1 + δ M G ) [ ε p + 2 ε h f ( ε p ε h ) ] ( 1 2 δ M G ) ,
ε MG = ε h [ ε p + 2 ε h + 2 f ( ε p ε h ) ] [ ε p + 2 ε h f ( ε p ε h ) ] .
R i = 1 ( 1 R e ) m 1 2 .
K = ξ n C abs ,
S = ξ n ( 1 σ c ) C sca ,
Q ext = 2 x 2 n = 1 ( 2 n + 1 ) Re ( a n + b n ) ,
Q sca = 2 x 2 n = 1 ( 2 n + 1 ) ( a n 2 + b n 2 ) ,
Q abs = Q ext Q sca ,
K = 3 f ξ Q abs 4 a , S = 3 f ξ ( 1 σ c ) Q sca 4 a ,
σ c = ( 0 1 p ( μ ) d μ ) ( 1 1 p ( μ ) d μ ) 1 ,
Z inR = μ 2 r ε 2 r tanh ( i 2 π d 1 λ μ 2 r ε 2 r ) ,
Z in ( I + R ) = Z 1 [ Z inR + Z 2 tanh ( i 2 π ( d 2 d 1 ) λ μ 1 r ε 1 r ) ] Z 1 + Z inR tanh ( i 2 π ( d 2 d 1 ) λ μ 1 r ε 1 r ) ,
R R = 20 lg Z inR 1 Z inR + 1 .
R I + R = 20 lg Z in ( I + R ) 1 Z in ( I + R ) + 1 .
ε = ε 0 [ Ω p 2 ω ( ω + i τ ) ] ,
f ( θ ) = ( T / / 2 + T 2 ) 2 0 arcsin ( 1 m 1 ) ( T / / 2 + T 2 ) 2 d θ ,

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